Traditional collection and processing of seismic reflection data begins with the separate generation of conventional pressure waves (P-waves) or shear waves (S-waves) followed by their separate recording on single component receivers, i.e receivers that have active elements that respond to motions of the reflected waves in only one direction. Assuming a vertically oriented seismic source, conventional P-waves travel down into the earth and are reflected from one (or more) geologic layers as P-waves. A spread of receivers whose active elements respond to vertically oriented elastic wave motion only, record the P-waves. Similarly, for shear wave exploration, S-waves produced by a horizontally oriented seismic source, are reflected from similar reflectors as S-waves, and are recorded by the spread of receivers in similar fashion except that the active elements of the receivers would respond to horizontally oriented wave motion exclusively.
Processing of either P-wave and/or S-wave data is further complicated by the fact that collection is usually carried out using common midpoint (CMP) "roll-along" methods. Such methods utilize overlapping spreads of receivers in combination with "forward rolled" sources along a line of survey to generate substantial numbers of "redundant" seismic traces. That is, the latter are redundant in that a certain number of traces can be associated with the same common center point lying midway between a plurality of respective source-receiver pairs that generated the traces in the first place. After application of time shifts to such traces (called static and dynamic corrections), a common midpoint (CMP) gather is created. Thereafter, the associated traces of that gather are stacked, to provide improved signal-to-noise characteristics.
(In regard to the importance of understanding the relationship between collection coordinates wherein traces are identified by either source-positions (s) and receiver-locations (g) coordinates along the line of survey, or by coordinates associated with source-to-receiver stations offset distance (f), and midpoint location (y) between respective source and receiver pairs, see, in detail, John F. Claerbout's book "FUNDAMENTALS OF GEOPHYSICAL DATA PROCESSING", McGraw-Hill, 1976 at pages 228 et seq.)
Even though the stacked gather of traces are enhanced (because of stacking), interpretations can still made difficult due to the fact that at boundaries between different rock types, partial conversion occurs between one wave type and another, assuming the angle of the incident wave is greater than zero. For example, a P-incident wave can be partially converted to an Sv-reflected wave. Or an Sv-incident wave can be partially converted to a P-wave reflected signal.
While the Zeoppritz equations determine the amplitudes of the reflected and converted waves, they have been seldom used by interpreters of geophysical data in spite of the fact that modern seismic reflection collection methods such as CMP methods, use long offsets and involve significant angle of incidence. Reason: for deeper reflectors, the angles of incident are relatively low and the velocity and density contrasts between layers are assumed to be small. See for example, page 21 et seq of Kenneth H. Waters' book "A TOOL FOR ENERGY RESOURCE EXPLORATION", John Wiley and Sons, 1978 for further edification.
In addition, the complexity involved in applying such equations to the many different energy levels associated with the various reflected waves for all angles of incidence and various material contrasts that exit in the field, can generate so much data as to simply overwhelm the interpreter. He may find it too difficult to apply the Zoeppritz equations on a systematic basis especially where the field data is collected by modern CMP methods. In this regard, even though center points/reflection points may not be vertically aligned, the interpreter usually ignores that fact, viz., ignores the differences that in converted P-wave to Sv-wave path lengths measured about vertical projections through center points midway between respective source-receiver pairs.
That is to say, with conventional incident and reflected waves, reflection points of flat, horizontal reflectors are located directly below the vertical projections of the midpoints of respective source-receiver pairs associated with the traces of interest. Thus, traces associated with common reflection points (or depth points) on flat reflectors, although from different source-receiver pairs can be summed (staked), after appropriate corrections to align the traces. But with converted waves under the same circumstances, the reflection points are not located below projections from the midpoints of respective source-receiver pairs but instead are displaced a certain distance from those projections.
The closest prior art that I am aware of that describes the problem of non-symmetrical path lengths is found in "DIGITAL PROCESSING OF TRANSFORMED REFLECTED WAVES", SOVIET GEOLOGY AND GEOPHYSICS, V. 21, No. 4, pp. 51-59.
T. T. Nedfedkina et al there describe use of P-wave to Sv-converted waves in permafrost regions of Siberia and like regions. A stacking procedure for such converted waves teaches the advantage of varying the stacking point of the gathers in accordance with a series of normalizing values associated with a special Soviet digital processing code called "Kondakova's alpha-language". But since the procedure uses exotic processing terminology, inferior data sets, and similistic models, conventional use of their work in the context of modern exploration methods especially where dipping reflectors are contemplated, has not been possible.